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 A306212 Numbers that are the sum of squares of three distinct positive integers in arithmetic progression. 2
 14, 29, 35, 50, 56, 66, 77, 83, 93, 107, 110, 116, 126, 140, 149, 155, 158, 165, 179, 194, 197, 200, 210, 219, 224, 242, 245, 251, 261, 264, 275, 290, 293, 302, 308, 315, 318, 332, 341, 350, 365, 371, 372, 381, 395, 398, 413, 428, 434, 435, 440, 450, 461, 462, 464, 482, 491, 504, 509, 515, 525, 530, 539, 557, 560, 563, 579, 590, 594, 596 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE 35 = 1^2 + 3^2 + 5^2, with 3 - 1 = 5 - 3 = 2; 371 = 1^2 + 9^2 + 17^2, with 9 - 1 = 17 - 9 = 8. Also 371 = 9^2 + 11^2 + 13^2, with 11 - 9 = 13 - 11 = 2. PROG (PARI) for(n=3, 600, k=sqrt(n/3); a=2; v=0; while(a<=k&&v==0, b=(n-3*a^2)/2; if(b==truncate(b)&&issquare(b), d=sqrt(b); if(d>=1&&d<=a-1, v=1; print1(n, ", "))); a+=1)) (PARI) w=List(); for(n=3, 600, k=sqrt(n/3); for(a=2, k, for(c=1, a-1, v=(a-c)^2+a^2+(a+c)^2; if(v==n, listput(w, n))))); print(vecsort(Vec(w), , 8)) CROSSREFS Cf. A000290, A000378, A000408, A085317, A120328, A292313, A306213, A306214. Sequence in context: A305662 A174070 A045527 * A041384 A041382 A047725 Adjacent sequences:  A306209 A306210 A306211 * A306213 A306214 A306215 KEYWORD nonn AUTHOR Antonio Roldán, Jan 29 2019 STATUS approved

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Last modified December 16 01:32 EST 2019. Contains 330013 sequences. (Running on oeis4.)